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Energy & Fuels 2003, 17, 338-343
Thermodynamic Properties of Synthetic Natural Gases. Part 3. Dew Point Curves of Synthetic Natural Gases and Their Mixtures with Water. Measurement and Correlation Susana Avila,† Sofı´a T. Blanco,‡ Inmaculada Velasco,‡ Evelyne Rauzy,§ and Santos Otı´n*,‡ Departamento de Innovacio´ n Tecnolo´ gica, Enaga´ s, S. A., Spain, Departamento de Quı´mica Orga´ nica y Quı´mica Fı´sica, Facultad de Ciencias, Universidad de Zaragoza, 50.009 Zaragoza, Spain, and Laboratoire de Chimie Physique de Marseille, Faculte´ des Sciences de Luminy. Universite´ de la Mediterrane´ e, 13.288 - Marseille Cedex 9, France Received June 5, 2002
Experimental measurements of dew points for eight synthetic natural gases (SNG) + water mixtures were carried out between (1.2 and 99.3) × 105 Pa in the temperature range from 226.4 to 287.6 K. The experimental results were analyzed in terms of both an equation of state model and an excess function-equation of state method, which reproduced the experimental data within AAD from 1.4 to 4.1 K and from 0.6 to 4.3 K, respectively.
Introduction
Experimental Section
Knowledge of the experimental water dew point in natural gases is important in the design of dehydration units to prevent the undesired formation of ice or hydrates and for the corrosion of the pipes or blockages during transport. To understand the influence of water on the vapor-liquid equilibrium of natural gases, which contain CO2, eight SNG + water mixtures were studied. The compositions of the five SNGs used are similar to those supplied through the Spanish pipeline network. In this work SNGs are used instead of real natural gas in order to separate the predictive capability of the theoretical models from the problems of the so-called C6+ fraction of natural gas on the liquid-vapor equilibrium calculations. A water dew point generation experimental apparatus was built and commissioned,1 and the dew point curves of the five dry SNG used in this work and their mixtures with water and methanol were obtained.2 The results on eight SNG + water mixtures at pressures from (1.2 to 99.3) × 105 Pa and temperatures from 226.4 to 287.6 K are presented here. The experimental results obtained on the multicomponent systems were analyzed in terms of both an equation of state (EOS) model and an excess functionequation of state (EOS) method, which reproduced the experimental data within an AAD from 1.4 to 4.1 K and from 0.6 to 4.3 K, respectively.
The experimental dew point ranges from (1.2 to 99.3) × 105 Pa at temperatures from 226.4 to 287.6 K. The five SNGs used in this work were prepared according to the gravimetric method3 by Air Liquide and Abello´sLinde. The compositions of these SNGs and their accuracy specified by the supplier are listed in Table 1. The dew point generation apparatus used for the collecting of the experimental data was described in a previous paper.1 The experimental method used for this work is based on the generation of saturated gases with water by condensation of this compound in two successive temperature-controlled condensers with continuous gas flow at specified pressures. After controlled expansion, the gas is saturated with water vapor by flowing through liquid water in an isolated saturator held at laboratory temperature. The temperature control of water condensation is then achieved in two successive stainless steel condensers. The first condenser temperature is set to a value lying between ambient and the temperature of the second condenser. Doing so, the quantity of liquid collected into the second condenser is minimized. The concentration of water in the gas is measured at the outlet of the dew point generation system, using a Karl Fischer titration, according to the standard method4 at atmospheric pressure. By doing so, the water content reference value of the gaseous phase is obtained. The dew point values of the SNG + water mixtures are measured by means of a chilled mirror instrument.5 The chilled mirror instrument input pressure is set using a regulator
* Corresponding author. Tel.: +34 976 761 199. Fax: +34 976 761 202. E-mail:
[email protected]. † Enaga ´ s, S. A. ‡ Universidad de Zaragoza. § Universite ´ de la Mediterrane´e. (1) Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. Fluid Phase Equilib. 1999, 161, 107-117. (2) Avila, S.; Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. Proc. 2001 Int. Gas Res. Conf. (IGRC) 2001, TP-17.
(3) Analyse des GazsPre´paration des Me´langes de Gaz pour E Ä talonnage. Me´thodes Ponde´rales. International Standard ISO 6142; 1981. International Organization of Standardization, Geneva, Switzerland. (4) Natural GassDetermination of Water by the Karl-Fischer Method. International Standard ISO 10101; 1993. International Organization of Standardization. Geneva, Switzerland. (5) Gas Analysis. Determination of the Water Dew Point of Natural Gas. Cooled Surface Condensation Hygrometers. International Standard ISO 6327; 1981. International Organization of Standardization, Geneva, Switzerland.
10.1021/ef020129p CCC: $25.00 © 2003 American Chemical Society Published on Web 02/14/2003
Thermodynamic Properties of Synthetic Natural Gases
Energy & Fuels, Vol. 17, No. 2, 2003 339
Table 1. Composition of Synthetic Natural Gases (% mol) and Absolute or Relative Accuracy Specified by the Supplier component
Gas 1
Gas 2
Gas 3
Gas 4
Gas 5
nitrogen CO2 methane ethane propane i-butane n-butane i-pentane n-pentane n-hexane n-heptane n-octane
0.618 ( 2% 0.187 ( 2% The rest 0.082 ( 2% 0.065 ( 2% 0.050 ( 2%
0.313 ( 2% 0.202 ( 2% The rest 8.038 ( 1% 0.801 ( 2% 0.081 ( 2% 0.123 ( 2% 0.010 ( 2% 0.0079 ( 2% 0.0047 ( 2% 0.0011 ( 2%
2.80 ( 0.06 0.20 ( 0.01 The rest 0.18 ( 0.01 0.1029 ( 0.0020 0.0499 ( 0.0010 0.0095 ( 0.0002 0.0166 ( 0.0004
6.90 ( 0.14 0.51 ( 0.01 The rest 2.72 ( 0.06 0.85 ( 0.02 0.17 ( 0.01 0.32 ( 0.01 0.0850 ( 0.0020 0.0940 ( 0.0020 0.119 ( 0.003 0.0258 ( 0.0006 0.0180 ( 0.0004
5.651 ( 1% 0.284 ( 2% The rest 7.526 ( 1% 2.009 ( 2% 0.305 ( 2% 0.520 ( 2% 0.120 ( 2% 0.144 ( 2% 0.068 ( 2% 0.0138 ( 2% 0.011 ( 2%
0.017 ( 2% 0.032 ( 2% 0.0027 ( 2% 0.0033 ( 2%
valve. When the apparatus reaches a stable value of dew temperature, both pressure and temperature are recorded. In this way, the values of the temperature and pressure of the dew point curve of the mixture generated are obtained. To analyze the contents of water and to carry out the dew point measurements the following instrumentation is used: • Mitsubishi CA 06 Karl Fischer Titrator, coupled with an Elster wet gasmeter Type Gr. 00, E51, 0.2% accuracy. • MBW Dew Point Instrument, model DP3-D-HP-K2. The cooling of the mirror is achieved by cascaded Peltier elements and the dew point mirror temperature is controlled optoelectronically. • Pressure Transmitter. With a maximum error of 0.1% in the calibrated range. Prior to this study of SNG + water dew points, the performance of both analytical methods and experimental procedures was checked. To obtain the precision of the analysis of water content, repeated analysis of water content of a standard nitrogen + water mixture prepared by Air-Liquide were carried out. The measured values were equal to the standard water content within a rejecting percentage of 0.05%.6 The absolute average deviation was of 0.5 × 10-6 kg m-3(n) for a mean value of water content of 59.0 × 10-6 kg m-3(n). The uncertainty of the water dew point measurement, given by the supplier of the MBW Dew Point Instrument was of (0.3 K for dew point temperatures between 198.2 and 228.2 K and of (0.2 K for dew point temperatures from 228.2 to 273.2 K. To evaluate the precision of the water dew point generation, repeated generation of methane + water mixtures were carried out. The test was achieved on a water dew point of 72 × 105 Pa and 258.1 K in pure methane. Water contents and dew point curves of each generated mixture were measured. The results obtained in the performance evaluation are the following: • For water content, the absolute average deviation was 1.0 × 10-6 kg m-3(n) for a mean value of water content of 19.6 × 10-6 kg m-3(n). • For dew point pressure, the relative average deviation was 3% on a range of pressure from (2.1 to 71.1) × 105 Pa. • For dew point temperature, the absolute average deviation was 0.4 K on a range of temperature from 225.8 to 259.1 K. Reference conditions for volume are 273.15 K and 1.01325 × 105 Pa.
Results The water contents in the vapor phase and the dew point data for the mixtures generated at the moisture (6) Statistical Interpretation of DatasTechniques of Estimation and Tests Relating to Means and Variances. International Standard ISO 2854; 1976. International Organization of Standardization, Geneva, Switzerland.
0.0160 ( 0.0004 0.0054 ( 0.0003 0.0038 ( 0.0002
generation system were determined and the results of the experiments are provided in Table 2. Theory Introduction. Equations of state such as the SantisBreedveld-Prausnitz EOS,7 the Nakamura-BreedveldPrausnitz EOS,8 the Peng-Robinson EOS,9 and the Robinson-Peng-Ng10 yield good results in the calculation of water dew points of natural gases at higher temperatures than those of the natural gas pipeline network. In this work a model based on a modified PengRobinson EOS11 is used in order to obtain a good description of water vapor pressure of ice and liquid water. This equation allows us to predict properly the water dew point curve in the usual temperature and pressure range of importance for natural gas pipelines. On the other hand, classical models such as UNIFAC,12 DISQUAC,13 or modified UNIFAC14 allow the prediction of the vapor-liquid equilibrium at low pressure for systems which contain a polar component but these models are not suited for high-pressure calculations. In this work an excess function-EOS method developed by Pe´neloux et al.15 founded on the zeroth order approximation of Guggenheim’s model is used. For the EOS-based models, available experimental binary systems data are required to calculate the interaction parameters. In the excess function-EOS methods, these parameters are calculated using a group contribution method. This makes it possible to predict dew point curves of real natural gases. This is important because not always does binary experimental data for all the components of the so-called C6+ fraction exist. Moreover, this work is part of a research study which aims to study the influence of the presence of methanol, as an additive of natural gas, in the water dew point of (7) de Santis, R.; Breedveld, G. J. F.; Prausnitz, J. M. Ind. Chem. Process Des. Dev. 1974, 13, 374. (8) Nakamura, R.; Breedveld, G. J. F.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. 1976, 15, 557. (9) Peng, D. Y.; Robinson, D. B. Can. J. Chem. Eng. 1976, 54, 595599. (10) Robinson, D. B.; Peng, D. Y.; Ng, H. Hydrocarbon Process. 1979, 58 (9), 269. (11) Althaus, K. Messung und Berechung von Wassergehalten Kohlenwasserstoffhaltiger Gasgemische. Doktors der Ingenieurwissenschaften (Dr.-Ing.). Fakulta¨t fu¨r Chemieingnieurwesen der Universita¨t Fridereciana zu Karlsruhe (Technische Hochschule) genehmigte, Germany, 1999. (12) Abrams, D. S.; Prausnitz, J. M. AIChE J. 1975, 21, 116-128. (13) Kehiaian, H. V. Fluid Phase Equilib. 1983, 13, 243-252. (14) Larsen, B. L.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 2274-2286. (15) Pe´neloux, A.; Abdoul, W.; Rauzy, E. Fluid Phase Equilib. 1989, 47, 115-132.
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Table 2. Experimental Dew Points Temperatures and Pressures for {SNG + Gjwater} Mixtures (Gjwater means the experimental value of water content obtained for each mixture) T/K
P/105
Pa
Gas 1, Fjwater ) 18.4 × 10-6 kg m-3 (n) 226.4 237.1 242.8 246.1 247.6 249.7 251.1 252.5 253.7 254.9 255.8 256.6 257.3 258.0 258.7
1.7 5.5 11.8 16.8 20.9 25.7 29.9 34.5 39.4 44.8 49.5 54.4 59.2 64.3 70.5
2.9 6.0 10.1 15.5 20.2 25.0 30.1 34.6 39.7 44.6 50.0 55.2 60.3 64.7 71.1
1.8 5.2 10.5 14.7 19.8 25.5 30.2 35.5 40.6 45.3 50.2 55.1 60.3 66.1 71.1
2.8 5.6 10.5 15.2 20.3 24.9 30.0 35.1 39.9 46.1 50.2 55.0 60.4 64.8 70.0
242.5 256.0 263.3 269.0 272.4 274.8 277.8 279.4 281.0 282.4 283.8 284.4 285.8 286.8 287.6
272.6 273.4 274.0 275.0 275.7 276.4 277.3
1 0.90544 -0.21378 0.26
Ref 11.
To evaluate these two models for the prediction of water dew points of multicomponent systems in the studied temperature and pressure ranges, a comparison between experimental and calculated values of dew temperature was carried out. The values of dew temperature of the vapor phase for the studied systems are calculated by means of both methods using the experimental values of pressure and composition obtained in the present work. Description of the EOS Model. The EOS model used in this work is based on a modified Peng-Robinson EOS11 in order to obtain a good description of water vapor pressure of ice and liquid water. The binary interaction parameters between the natural gas components and water were also obtained. The equation of state used is the Peng-Robinson cubic equation of state9 of the form:
P)
RT a v - b v2 + 2bv - b2
(1)
with
b(T) ) b(Tc) and a(T) ) a(Tc) R(Tr,ω)
(2)
where
R1/2 ) 1 + κ(1 - Tr1/2) and In the case of water the following equation is used:11
1.2 4.1 7.4 12.1 17.0 22.7 30.3 34.7 39.8 44.7 49.9 54.5 60.1 65.3 69.5
Gas 5, Fjwater ) 72.1 × 10-6 kg m-3 (n) 83.1 88.1 92.4 95.2 99.3
0.77404 1.58484 0 -2.28241
κ ) 0.374640 + 1.54226ω - 0.26992ω2 (3)
Gas 4, Fjwater ) 190.7 × 10-6 kg m-3 (n)
Gas 5, Fjwater ) 15.6 × 10-6 kg m-3 (n) 260.1 260.7 261.8 261.9 261.9
236.3 246.7 253.5 255.7 260.2 263.3 265.3 267.2 268.7 269.3 270.3 271.2 272.2 273.1 273.9
A0 A1 A2 A3 a
1.9 5.2 10.2 15.1 20.0 24.8 31.1 35.5 39.9 44.9 49.9 54.5 60.0 65.2 70.4
Gas 2, Fjwater ) 69.9 × 10-6 kg m-3 (n)
Gas 3, Fjwater ) 21.7 × 10-6 kg m-3 (n) 231.3 237.3 244.2 247.3 250.0 252.0 253.9 255.4 256.7 258.1 259.5 260.4 261.1 261.6 262.2
233.8 243.9 250.5 254.3 257.5 259.5 261.8 263.2 264.3 265.2 266.1 266.9 268.0 268.9 269.8
coefficient 223.15 K e T < 273.15 K 273.15 K e T e 313.15 K
Pa
Gas 1, Fjwater ) 53.3 × 10-6 kg m-3 (n)
Gas 2, Fjwater ) 23.9 × 10-6 kg m-3 (n) 230.5 238.5 245.1 249.4 252.4 254.2 256.0 257.3 258.9 259.9 261.1 262.3 262.9 263.4 264.2
T/K
P/105
Table 3. Values of the Coefficients A0, A1, A2, and A3 Used in the EOS Modela
R1/2 ) A0 + A1(1 - Tr1/2) + A2(1 - Tr1/2)2 + A3(1 - Tr1/2)4 (4) Different values for coefficients A0, A1, A2, and A3 are used for T > 273.15 K and for T < 273.15 K (Table 3). For calculation of parameters a and b in the case of mixtures, classical mixing rules are used of the following form:11 n
a)
xixjaij ∑ i)1
and aij ) xaiaj(1 - kij)
(5)
n
b) 64.4 69.1 72.7 78.8 83.7 89.1 95.8
natural gases.2,16 The excess function-EOS method used in this work allows to be modified to have into account the self-association of methanol in the mixtures.
xi b i ∑ i)1
with kij ) kji, and kii ) kjj ) 0
(6)
Due to the change of the function R for water, new binary interaction parameters for natural gas components and water were obtained.11 In the case of CO2 + H2O, CH4 + H2O, and C2H6 + H2O, the following (16) Avila, S.; Blanco, S. T.; Velasco, I.; Rauzy, E.; Otı´n, S. Thermodynamic Properties of Synthetic Natural Gases. Part 2. Dew Point Curves of Synthetic Natural Gases and their Mixtures with Water and Methanol. Measurement and Correlation. Energy Fuels, in press.
Thermodynamic Properties of Synthetic Natural Gases
Energy & Fuels, Vol. 17, No. 2, 2003 341
Table 4. Values of the Temperature-Independent Part of the Binary Interaction Parameters, kij,0, Used in Eq 7 for the EOS Model N2 H2O CO2 CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12 n-C6H14 a
N2
H2O
CO2
CH4
C2H6
C3H8
0 0.4800 -0.0170 0.0311 0.0515 0.0852 0.1033 0.0800 0.0922 0.1000 0.1496
0 0.1840 0.6510 0.6350 0.5300 0.6900 0.6900 0.5000 0.5000 0.5000
0 0.0919 0.1322 0.1241 0.1200 0.1333 0.1219 0.1222 0.1100
0 -0.0026 0.0140 0.0256 0.0133 -0.0056 0.0230 0.0422
0 0.0011 -0.0067 0.0096 0.0160 0.0078 -0.0100
0 -0.0078 0.0033 0.0111 0.0267 0.0007
i-C4H10
n-C4H10
0 -0.0004
i-C5H12
n-C5H12
0 0.0600
0
n-C6H14
0 0.0174 -0.0056
0
Ref 11.
Table 5. Values of the Temperature-Dependent Part of the Binary Interaction Parameters, kij,1, Used in Eq 7 for the EOS Modela N2 H2O CO2 CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12 n-C6H14 a
N2
H2O
CO2
CH4
C2H6
C3H8
i-C4H10
n-C4H10
i-C5H12
n-C5H12
n-C6H14
0 0 0 0 0 0 0 0 0 0 0
0 0.2360 -1.3850 -0.9300 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0
0 0
0
Ref 11.
temperature function has to be used:
kij(T) ) kij,0 + kij,1
T - 1) (273.15
where
Values for the binary interaction parameters kij,0 and kij,1 used in this work are given in Tables 4 and 5. Description of the Excess Function-EOS Model. To represent the vapor-liquid equilibrium of the mixtures studied, a model founded on the zeroth approximation of Guggenheim’s reticular model was selected. The model satisfies two important conditions: (1) The Helmholtz energies of pure components are calculated by an equation of state. (2) The excess functions are obtained at constant packing fraction, η. This means that the value of the packing fraction, η, for each component in the mixture is the value of the pure component. This assumption leads to
η)
b bi (i ) 1, ..., p) ) v vi
(8)
The molar Helmholtz energy of a mixture, A, may be written as follows:
xiai A ) Aid - RT ln(1 - η) Q(η) + AEres b i)1 i p
∑
(9)
where Aid is the ideal mixture molar Helmholtz energy, ai is the attractive parameter of component i of a translated Peng-Robinson cubic equation of state,17,18 bi is the covolume of component i, AEres is the residual excess Helmholtz energy, and Q(η) is expressed as follows:
Q(η) )
∫0η
Q′(η) dη η
Q′(η) )
(7)
(10)
η and γ ) 2(x2 + 1) 1 + γη
(11)
AEres is written by means of a formalism that enables us to separate the composition and packing fraction variables:
AEres ) E(T,x) Q(η)
(12)
For the first term on the right-hand side of eq 12 the following equations are used:19
E(T,x) )
1
p
[
2qm
p
p
p
1/3 qixi[∑qjxjKij] + ∑qixi[∑q1/3 ∑ j xjLji ]] i)1 j)1 i)1 j)1
(13)
with
Kij )
E1ij + E2ij and Lij ) E2ij - E1ij, Lij ) - Lji (14) 2 p
qm )
∑ qkxk and qk ) δkbk k)1
(15)
where the subscripts i and j refer to the components i and j of the mixture with p components, qi is the molecular surface of the component i. It is assumed that (17) Pe´neloux, A.; Rauzy, E.; Fre´ze, R. Fluid Phase Equilib. 1982, 8, 7-23. (18) Rauzy, E. Les Me´thodes Simples de Calcul des EÄ quilibres Liquide-Vapeur Sous Pression. The`se d’Etat-Sciences.Universite´ Aixs Marseille II, France, 1982. (19) Hocq, H. Etude Expe´rimentale et Mode´lisation Thermodynamique des Me´langes Me´thanol-Eau-Hydrocarbures. The`se en Sciences. Universite´ de Droit, d’Economie et des Sciences d′AixsMarseille III, France, 1994.
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Figure 1. Experimental dew point curve2 of gas 1 (b) and comparison between experimental dew point curves (symbol) and calculated with the EOS model (dotted line) and with the excess function-EOS method (line) for the systems: (9) gas 1 + 18.4 × 10-6 kg m-3(n) water, (0) Gas 1 + 53.3 × 10-6 kg m-3(n) water.
Figure 2. Experimental dew point curve2 of gas 2 (b) and comparison between experimental dew point curves (symbol) and calculated with the EOS model (dotted line) and with the excess function-EOS method (line) for the systems: (9) gas 2 + 23.9 × 10-6 kg m-3(n) water, (0) gas 2 + 69.9 × 10-6 kg m-3(n) water.
(qi/qj) ) ((bi/bj))δ. δ is an adjustable parameter. Kij and Lij are two binary interaction parameters between components i and j, which are calculated from eq 14. The interchange energies, E1ij and E2ij, are calculated using a group contribution method as follows:19
E1ij ) -
1
N N
∑ ∑(Rik - Rjk)(Ril - Rjl)A1kl(T)
2k)1l)1
with A1kl ) 1A0kl E2ij ) -
1
() T
0
0
1Bkl
(16)
T
N N
∑ ∑(Rik - Rjk)(Ril - Rjl)A2kl(T) 2k)1l)1 with A2kl ) 2A0kl
() T0 T
0
2Bkl
(17)
Figure 3. Experimental dew point curve2 of gas 3 (b) and comparison between experimental dew point curves (symbol) and calculated with the EOS model (dotted line) and with the excess function-EOS method (line) for the system: (9) gas 3 + 21.7 × 10-6 kg m-3(n) water.
where 1A0kl, 1B0kl, 2A0kl, and 2B0kl are group interaction parameters. Discussion In this work the influence of water and usual components of natural gas on vapor-liquid equilibrium of natural gases imported in Spain through European and Magreb gas pipeline networks has been studied. The experimental dew points curves and calculated with both an EOS model and excess function-EOS method are represented in Figures 1-5. No experimental evidence of hydrates presence, as blockages in the experimental device, has been observed. The experimental dew point curves of dry SNG mixtures obtained in other work2 are also represented in order to better explain the influence of the presence of water in the dew points curves of natural gas which contain water. As can be seen in Figures 1-5 an increase of water content in the studied SNG+water mixtures shows a displacement of the dew point to higher values of temperatures and pressures. From the obtained hydrocarbon dew point curves of studied SNG’s it can be concluded that these SNG’s have high risk of potential condensation, specially Gas 4 and Gas 5. When water contents from (15.6 to 190.7) ×
Figure 4. Experimental dew point curve2 of gas 4 (b) and comparison between experimental dew points curves (symbol) and calculated with the EOS model (dotted line) and with the excess function-EOS method (line) for the system: (9) gas 4 + 190.7 × 10-6 kg m-3(n) water.
10-6kg m-3(n) are added to these two SNG’s, the risk of condensation is only increased at high pressures. A comparison between experimental and calculated values was carried out and the results obtained for each dew point curve are presented in Table 6. The results are quite good with values of AAD of dew point temperature between 1.4 and 4.1 K with the EOS model and from 0.6 to 4.3 K for excess function-EOS method.
Thermodynamic Properties of Synthetic Natural Gases
Energy & Fuels, Vol. 17, No. 2, 2003 343 Table 6. Values of AAD1 (EOS Model) and AAD2 (Excess Function-EOS Method) and Experimental Ranges of Dew Temperatures and Pressures for Multicomponent {SNG+GjWater} Mixtures (Gjwater means the experimental value of water content obtained for each mixture) SNG Fjwater/10-6 mixture kg m-3(n) Gas 1 Gas 1 Gas 2 Gas 2 Gas 3 Gas 4 Gas 5 Gas 5
Figure 5. Experimental dew point curve2 of gas 5 (b) and comparison between experimental dew points curves (symbol) and calculated with the EOS model (dotted line) and with the excess function-EOS method (line) for the systems: (9) gas 5 + 15.6 × 10-6 kg m-3(n) water, (0) gas 5 + 72.1 × 10-6 kg m-3(n) water.
In the EOS model and influence of water content in AAD values is observed. The greatest deviations occur for the mixtures with the lowest water contents. It can be due to the experimental error in the water content analysis at very low water contents. No influence of pressure and temperature is found for the values of the AAD for both theoretical models. For the systems studied, the introduction of a group contribution method, as is used in case of excess function-EOS model, does not impair predictions respect to the EOS method with interaction parameters obtained from binary experimental data. It makes the excess function-EOS model very useful to predict the water dew point of real natural gases, provided that,
18.4 53.3 23.9 69.9 21.7 190.7 15.6 72.1
T range/K
P range/ 105 Pa
226.4-258.7 233.8-269.8 230.5-264.2 236.3-273.9 231.1-262.2 242.5-287.6 260.1-261.9 272.6-277.3
1.7-70.5 1.9-70.4 2.9-71.1 1.8-71.1 2.8-70.0 1.2-69.5 83.1-99.3 64.4-95.8
AAD1/ AAD2/ K K 1.8 1.4 4.1 2.0 3.4 3.2 2.9 2.1
1.1 1.2 4.3 3.5 1.3 2.4 0.6 2.1
not always binary experimental data for all components of the so-called C6+ fraction exist. Appendix For comparison between calculated and experimental dew point temperatures for each studied dew point curve we used the deviation
AAD )
1
N
|Texp - Tcal ∑ i i | Ni)1
where N is the number of dew points that constitute a dew point curve. Acknowledgment. The authors acknowledge financial and technical support from Enaga´s, S. A. during the experimental part of this work. EF020129P
